So, I'm guessing that one can write a script to clone the Default profile on the fly, change it's *background_color*, invoke gnome-terminal with this profile, and delete the profile before exiting. You'll also need a database of good foreground/background color combinations for this script to use.

Update: Here is a script to do what is discussed above. It does not generate a random background color, that you'll have to generate using some list.